Shyam Keralavarma

A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented. The dislocations are modeled as line singularities embedded in a linear elastic medium while the point defects are represented by a concentration field as in continuum diffusion theory. Plastic flow arises due to the collective motion of a large number of dislocations. Both conservative (glide) and nonconservative (diffusion-mediated climb) motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep, recovery and relaxation in crystalline materials. With emphasis laid on lattice vacancies, the creep response of planar single crystals in simple tension emerges as a natural outcome in the simulations. A large number of boundary-value problem solutions are obtained which depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep. In addition, some unique experimental aspects of creep in small scale specimens are also reproduced in the simulations.

An isotropic multi-surface model of porous material plasticity is derived and employed to investigate the effects of the third stress invariant in ductile failure. The constitutive relation accounts for both homogeneous and inhomogeneous yielding of a material containing a random distribution of voids. Individual voids are modeled as spheroidal but the aggregate has no net texture. Ensemble averaging is invoked to operate a scale transition from the inherently anisotropic meso-scale process of single-void growth and coalescence to some macroscopic volume that contains many voids. Correspondingly, expressions for effective yield and associated evolution equations are derived from first principles, under the constraint of persistent isotropy. It is found that the well-known vertex on the hydrostatic axis either disappears for sufficiently flat voids or develops into a lower-order singularity for elongated ones. When failure is viewed as the onset of an instability, it invariably occurs after the transition to inhomogeneous yielding with the delay between the two depending strongly upon the Lode parameter. The strain to failure is found to be weakly dependent on the Lode parameter for shear-dominated loadings, but strongly dependent on it near states of so-called generalized tension or compression. Experimentally determined fracture loci for near plane stress states are discussed in light of the new findings.

The objective of this paper is to perform numerical assessment of a micromechanical model of porous metal plasticity developed previously by the authors. First, upper bound estimates for the yield loci are computed using homogenization and limit analysis of a spheroidal representative volume element containing a confocal spheroidal void, neglecting elasticity. Unlike in the development of the analytical model, the computational limit analysis is performed without recourse to approximations so that the obtained yield loci are rigorous upper bounds for the true criterion. Next, the model's macroscopic dilatancy at incipient plastic flow is compared against that of the numerical limit analysis approach. Finally, finite-element calculations, with elasticity included, are presented for transversely isotropic porous unit-cells loaded axisymmetrically. The effective stress-strain response as well as evolution of the unit-cell porosity and void aspect ratio are compared with theoretical predictions.